should i give her a chance ?

You seem like you don't know the psychology of a woman's brain. Most women like keeping men on a leash. For example, she told you that she doesn't want to be with you just so you'd want her more. But after she noticed that you didn't come back to her, she apologized.

The closer you get to a female, the more she pushes you away. The further you get from a female, the more she begs you to come back to her.

You need to tell her that you're not her "play thing", her dog on her leash or anything like that.

If she then starts acting like crap to you then leave her immediately. She is NOT worth it since she's essentially treating you like a dog.

my son is going through this now ,he went out with a girl for about 9mth then some stories kicked off with her girl friends about my son so this girl dropped my son ,after a while she came back saying she now knows it was her friends being jealous ,but my son as i tell all my grown children don't be second best,he told her sorry he can't as he would always be questioning him self?

he just met a lovely girl before summer she has a fellow but they don't get on so she wants to be with my son ,but she won't give her fellow up to be with him ,she has asked for time she has had time to much infarct ,they went to a prom together my son stayed with his mates as he thought it was her fellows place to be with her ,he never showered be side her stayed with his mates all night ,so then she said i never saw your son that's because he stayed out the way ,now he has seen the light even though he likes her he said he won't be second best his worth more than that ,so his enjoying life now and what will be is what will be

sounds like someone is playing games ,and knows just how to work round you ,can you trust her is what you should be asking your self ?

if not then i would not bother good luck

Nah, find someone else man. i know much easier said than done. but she does not seem like the right girl.